◆ SEQUENCE AND SERIES ◆
[tex]\\ given \: expression \: - \\ \\ (1 - \frac{1}{6} ) \times (1 - \frac{1}{7} ) \times (1 - \frac{1}{8} ) \times ....... \times (1 - \frac{1}{100} ) \\ \\ ( \frac{6 - 1}{6} ) \times ( \frac{7 - 1}{7} ) \times ( \frac{8 - 1}{8} ) \times ....... \times ( \frac{100 - 1}{100}) \\ \\ \frac{5}{6} \times \frac{6}{7} \times \frac{7}{8} \times \frac{8}{9} \times ....... \times \frac{98}{99} \times \frac{99}{100} \\ \\ as \: we \: can \: see \: \: , \\ \: \\ the \: numbers \: cancel \: each \: other \: diagonally \\ \\ leaving \: only \: \: , \\ \\ \frac{5}{1} \times \frac{1}{100} \\ \\ \\ = \frac{5}{100} \\ \\ \\ = \frac{1}{20} \: \: \: \: \: ans.[/tex]
